Cryptology ePrint Archive: Report 2009/448

Precise Bounded-Concurrent Zero-Knowledge in Almost Constant Rounds

Ning Ding and Dawu Gu and Bart Preneel

Abstract: Precise concurrent zero-knowledge is a new notion introduced by
Pandey et al. \cite{P:P:M:T:V} in Eurocrypt'08 (which generalizes
the work on precise zero-knowledge by Micali and Pass \cite{M:P} in
STOC'06). This notion captures the idea that the view of any
verifier in concurrent interaction can be reconstructed in the
almost same time. \cite{P:P:M:T:V} constructed some (private-coin)
concurrent zero-knowledge argument systems for $\NP$ which achieve
precision in different levels and all these protocols use at least
$\omega(\log n)$ rounds. In this paper we investigate the
feasibility of reducing the round complexity and still keeping
precision simultaneously. Our result is that we construct a
public-coin precise bounded-concurrent zero-knowledge argument
system for $\NP$ only using almost constant rounds, i.e.,
$\omega(1)$ rounds. Bounded-concurrency means an a-priori bound on
the (polynomial) number of concurrent sessions is specified before
the protocol is constructed. Our result doesn't need any setup
assumption. We stress that this result cannot be obtained by
\cite{P:P:M:T:V} even in bounded-concurrent setting.